Prepare the lamb
Position a rack in the center of the oven and heat the oven to 350°F.
Season the lamb with 2 tsp. salt and 1/2 tsp. pepper. In a 5- to 6-quart Dutch oven, combine the lamb, carrots, onion, cinnamon, bay leaf, and enough water to cover. Cover and braise in the oven until the meat is very tender, about 2-1/2 hours. Strain the mixture through a fine sieve over a large bowl. Discard the vegetables and spices. (The recipe may be prepared to this point up to 2 days ahead. Cool the lamb and broth, and refrigerate separately. Skim the fat from the broth before continuing.)
Make the stew
In a 5- to 6-quart Dutch oven, heat the butter or oil over medium-high heat. Add the onion, a pinch of salt, and a few grinds of pepper and cook, stirring occasionally, until softened and lightly browned, about 8 minutes. Add the garlic, paprika, cumin, coriander, and cayenne and cook, stirring occasionally, until fragrant (don’t let the garlic burn), 1 to 2 minutes.
Stir in the chickpeas, prunes, tomato purée, and a pinch of salt. Add the reserved lamb and 4 cups of the broth and bring to a boil. Boil for 5 minutes and then turn the heat to low. Cover and simmer for 10 minutes. Add the parsnips and cook until tender, about 10 minutes. Season to taste with salt and pepper, and serve sprinkled with cilantro or parsley.